Due to the high computational complexity and long convergence time of SPSA, we make an ordering assumption on the power codebook entries and derive effective hyperplane based approximations to the channel quantization regions and present a number of low-complexity suboptimal quantized power codebook design algorithms.
The density of expression values for each gene in each tissue type was calculated (Additional file 2A-B) as follows: For computational efficiency we used fast Fourier transformation based approximation to calculate kernel density estimates (R 2.7.2 [ 47]).
Based on this, it is straightforward to compute the sample-based approximation to the marginal posterior probability that a measured peak is assigned to any formula/adduct/isotope combination (described here as an annotation).
The approach offers a rational, constraint-based approximation to the metabolic potential of a poorly characterized microbial consortium.
Instead, we assess the quality of the ABC-based approximation to the posterior using auxiliary simulation as illustrated in Figures 2– 4 comparing predicted to actual coverage probabilities and using RMSEs as in Table 1.
Related to the gene flow factor of Bengtsson (1985), relative reproductive rate is the central quantity in a coalescent-based approximation to the evolutionary process at neutral sites in a genome subject to incompatibility selection.
Due to the complexity of the problem, we propose a dynamic programming based approximation approach to find efficient solutions under given constraints.
Third, the CPBA model naturally generalizes network approximations that are already part of scientific practice, namely, the propensity based approach in multigraph models, the conformity decomposition in weighted networks, and the eigenvector based approximation in correlation networks.
The current paper introduces the CPBA model (cluster and propensity based approximation) for general similarity measures and sketches an efficient MM algorithm for estimation of the CPBA parameters.
The preconditioner proposed here combines the optimal sine transform based approximation with a layered medium model.
Furthermore, as shown below, in physiologically relevant regimes the fluctuation-dissipation based approximation is highly accurate and in some cases reduces to the Fano factor obtained by exactly solving the master equation.
